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Applied Thermal Engineering 24 (2004) 471–485 www.elsevier.com/locate/apthermeng

Thermoeconomic optimization of small size central air conditioner G.Q. Zhang *, L. Wang, L. Liu, Z. Wang College of Civil Engineering, Hunan University, Changsha, Hunan 410082, China Received 10 June 2003; accepted 10 October 2003

Abstract The application of thermoeconomic optimization design in an air-conditioning system is important in achieving economical life cycle cost. Previous work on thermoeconomic optimization mainly focused on directly calculating exergy input into the system. However, it is usually difficult to do so because of the uncertainty of input power of fan on the air side of the heat-exchanger and that of pump in the system. This paper introduces a new concept that exergy input into the system can be substituted for the sum of exergy destruction and exergy output from the system according to conservation of exergy. Although it is also difficult for a large-scale system to calculate exergy destruction, it is feasible to do so for a small-scale system, for instance, villa air conditioner (VAC). In order to perform thermoeconomic optimization, a program is firstly developed to evaluate the thermodynamic property of HFC134a on the basis of Martin– Hou state equation. Authors develop thermodynamic and thermoeconomic objective functions based on second law and thermoeconomic analysis of VAC system. Two optimization results are obtained. The design of VAC only aimed at decreasing the energy consumption is not comprehensive. Life cycle cost at thermoeconomic optimization is lower than that at thermodynamic optimization.
2003 Elsevier Ltd. All rights reserved. Keywords: Thermoeconomic optimization; Small size central air conditioner; Exergy destruction; Objective function; Life cycle cost

*

Corresponding author. Tel.: +86-731-8823900; fax: +86-731-8821005. E-mail address: [email protected] (G.Q. Zhang).

1359-4311/$ - see front matter
2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2003.10.009

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Nomenclature A heat transfer area (m2 ) C cost (RMB Yuan) COP coefficient of performance ideal gas heat capacity (kJ/kg K) CP0 Cp specific heat capacity (kJ/kg K) h specific enthalpy (kJ/kg) m mass flow rate (kg/s) N operating hours per year (h) P pressure (kPa) PI input power (W) critical pressure (4063.5 kPa) Pc Pr ¼ P =Pc relative pressure ratio Q heat or cooling capacity (kJ) r refrigerant s specific entropy (kJ/kg K) TDO thermodynamic optimization TEO thermoeconomic optimization T temperature (K) critical temperature (374.24 K) Tc Tr ¼ T =Tc relative temperature ratio T  ¼ 1  Tr dimensionless VAC villa air conditioner W power (W) Greeks q density (kg/m3 ) qc critical density (508 kg/m3 ) qr ¼ q=qc relative density ratio gm mechanical efficiency isentropic compression efficiency gsc Ds entropy rise (kJ/kg K) Subscripts a air con condenser coni air flowing into condenser cono air flowing out of condenser eva evaporator evai water flowing into evaporator evao water flowing out of evaporator FC fan coil

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FCi FCo g l w

473

air flowing into FC air flowing out of FC gas liquid water

1. Introduction Since the first small-size central air conditioner appeared in 1995, villa air conditioner (VAC) has developed rapidly in China. VAC is suitable for houses and apartments with floor area between 100 and 600 m2 . Because of the advantages of energy-saving, coziness, good appearance and longevity, many customers regard it as a favorable choice. However, its initial investment is higher than traditional house-hold air conditioners as split type and window type. Therefore, it is necessary to optimize the design of the VAC system in order to reduce the initial investment, and also the operating and maintenance cost. Thermodynamics and thermoeconomics methodologies were widely used in optimization design of air-conditioning system. Franco et al. conducted a thermodynamic optimization study using the model of a tube-by-tube evaporator with zeotropic refrigerant mixtures to evaluate the total exchanger irreversibility function and its various components [1]. Prakash performed thermodynamic and thermoeconomic analysis of a combined heat and power (CHP) system by numerical iteration technique [2]. Lee et al. applied thermoeconomics to study single-, double-, and triple-effect absorption chillers with a given cooling capacity to evaluate the specific life cycle costs of the systems and their auxiliary equipment [3]. In this paper, both thermodynamics and thermoeconomics are applied to optimize VAC system. Thermodynamic optimization results are compared with thermoeconomic optimization ones.

2. Calculation of the thermodynamic properties Thermodynamic property of refrigerant is a key factor to evaluate the system performance, so a program code concerning thermodynamic property of HFC134a is firstly developed. As a long-period substitute for CFCs, the refrigerant HFC134a owns good thermodynamics properties, in addition to its zero ODP. At present, many studies have been performed to investigate its thermodynamic properties. Wilson and Basu presented Martin–Hou (MH) state equation, saturated vapor pressure correlation, liquid density correlation, ideal gas heat capacity correlation and critical constant of HFC134a basing on experimental data [4]. Piao et al. obtained the experimental data concerning the PVT properties of HFC134a in an extensive range of temperatures, pressures, and densities by means of the constant volume method [5]. Piao et al. not only developed an 18-coefficient modified Benedict–Webb–Rubin (BWR) equation of state for HFC134a, but also presented new correlations of vapor pressure and saturated liquid density [6]. Piao extended the range of pressure and temperature to make results more precise, but PiaoÕs BWR state equation is more complicated than WilsonÕs MH state equation. This

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paper presents new formulas to calculate the thermodynamic properties basing on WilsonÕs and PiaoÕs work. 2.1. P –T equation of saturated state The correlation between pressure and temperature of refrigerant can be expressed as follows [6] h i ð1Þ lnðPr Þ ¼ 1=Tr a1 T  þ a2 ðT  Þ1:2 þ a3 ðT  Þ2 þ a4 ðT  Þ3 where a1 ¼ 7:97699, a2 ¼ 1:20977, a3 ¼ 0:889878, a4 ¼ 4:08932: 2.2. Specific volume equation of saturated liquid The following equation is introduced for calculating the specific volume of saturated liquid of HFC134a [6]: qr ¼ 1 þ b1 ðT  Þ0:3 þ b2 ðT  Þ0:6 þ b3 ðT  Þ1:2 þ b4 ðT  Þ2

ð2Þ

where b1 ¼ 1:29632, b2 ¼ 1:70615, b3 ¼ 0:827775, b4 ¼ 0:871639: 2.3. MH equation of state For its high precision, the MH equation of state has been successfully used to calculate all of the properties for many working fluids. MH equation of state for HFC134a can be expressed as follows [4]: P¼

5 30:498589Tr X Ai þ Bi þ Ci eð5:475Tr Þ þ i mb ðv  bÞ i¼2

ð3Þ

where coefficient b is 0.3455467 · 103 and Ai , Bi , Ci are listed in Table 1. 2.4. Ideal gas heat capacity The isobaric specific heat capacity of ideal gas is shown as follows [6]: CP0 ¼ 0:164523 þ 1:047011Tr  0:311364Tr2 þ 0:057919Tr3

ð4Þ

Table 1 Value of coefficients in Eq. (3) i

2

Ai Bi Ci

)0.1195051 0.1137950 · 103 )3.531592

3

4 3

0.1447797 · 10 )0.8942552 · 107 0.6469248 · 102

5

)1.049005 · 10 0 0

7

)6.953904 · 1012 1.269806 · 1013 )2.051369 · 109

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2.5. Saturated or superheat vapor enthalpy h ¼ h0 þ Pc Pr m þ 31:127444Tr þ 195:932404Tr2  38:844747Tr3 þ 5:419149Tr4 ! 4 4 X X Aiþ1 Ciþ1 þ i þ expð5:475Tr Þð1 þ 5:475Tr Þ i i¼1 iðm  bÞ i¼1 iðm  bÞ

ð5Þ

2.6. Saturated or superheat vapor entropy S ¼ S0 þ 0:0814882 lnð3:322286ðm  bÞ=Tr Þ þ 0:164523 lnð374:27Tr Þ þ 1:047011Tr ! 4 X Biþ1 2 3 þ 0:0146285 expð5:475Tr Þ  0:155682Tr þ 0:0193063Tr  i i¼1 iðm  bÞ ! 4 X Ciþ1  i i¼1 iðm  bÞ

ð6Þ

Eqs. (5) and (6) are derived from Eqs. (1,3) and (4), and saturated or superheated vapor enthalpy (entropy) is evaluated by means of Eq. (5) [6]. h0 and s0 are enthalpy and entropy at a reference state of the saturated state respectively. 2.7. Clapeyron equation The Clapeyron equation is given as follows in the saturated state: dP =dT ¼ ðhg  hl Þ=½T ðvg  vl Þ dP =dT ¼ ðsg  sl Þ=ðvg  vl Þ

ð7Þ ð8Þ

where dP =dT is the slope of the saturation liquid line, and can be gained through differentiating Eq. (3). Saturated vapor specific volume vg can be achieved from Eq. (3) by Newton iteration method, and liquid specific volume vl by Eq. (2), therefore, we can get saturated vapor enthalpy hg and entropy sg by Eqs. (5) and (6). So saturated liquid enthalpy and entropy are derived as Eqs. (7) and (8). 2.8. Saturated liquid enthalpy h i hl ¼ hg  Pc Pr ðm  ml Þ ln Pr þ a1 þ 1:2a2 ðT  Þ0:2 þ 2a2 T  þ 3a4 ðT  Þ2

ð9Þ

2.9. Saturated liquid entropy i h sl ¼ sg  10:857135ðPr =Tr Þðm  ml Þ ln Pr þ a1 þ 1:2a2 ðT  Þ0:2 þ 2a2 T  þ 3a4 ðT  Þ2

ð10Þ

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To calculate these thermodynamic properties, we have programmed a code using Visual C++ in terms of Eqs. (1)–(8). To validate the accuracy of the present code, the results have been compared to the previous studies [4,5]. A good agreement has been achieved with the average relative errors within ±1.2%. So the program can be introduced as a reference to the research of refrigeration machine, heat pump and the optimal design of the components or system and the development of the new products.

3. Second law analysis of VAC system Fig. 1 shows a VAC system, whose cooling capacity is 30 kW. VAC consists of a compressor, a condenser, an expansion apparatus, an evaporator and three fan coils (FC) which are in parallel. The evaporator supplies three fan coils with chilled water, and heat capacity is rejected by air flowing out of the condenser. The exergy of a working fluid in an open system indicates the maximum work the working fluid provides through a reversible process when it comes to equal with the environment. On the assumptions that the change of kinetic energy and potential energy is negligible, and that the environment temperature is T0 , the exergy of a unit mass can be expressed as Ex ¼ mðh  h0 Þ  T0 mðs  s0 Þ

ð11Þ

In the VAC system, according to the conservation of exergy, total exergy destruction yields as follows: Exin ¼ DEx þ Exout

ð12Þ

FC 1

FC 2

FC 3 pump

valve

4

valve

compressor

3 2

expansion valve

evaporator

condenser

valve

1

Fig. 1. Configuration of a VAC system.

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where Exin is the sum of exergy input from the system, which includes power of coil fans, power of chilled water pump, power of condenser fan, power of compressor and exergy of air flowing into coil fans. It should be noted that all electric energy input from outside the system is completely transferred into exergy, but that all heat energy is not completely transferred into exergy, because the heat energy that the air flowing through the condenser obtains is rejected into the atmosphere, exergy is zero. DEx is exergy destroyed from the system. Exout is the sum of exergy output from the system, which only includes exergy of air flowing out of fan coils. When the refrigerant performs the non-isentropic compression process (4–1) at the compressor, the compressor exchanges heat with the atmosphere, so it is difficult to calculate the entropy generation directly. However, by means of conservation of exergy for the steady-state process, taking the compressor as a control volume, entropy generation can be calculated, which is shown as follows: DExcom ¼ gm PI þ Excomi  Excomo

ð13Þ

Substituting Eq. (12) into Eq. (13) yields entropy generation equation (14) as follows: DScom ¼ gm PI=T0 þ mr ðh4  h1 Þ=T0 þ mr ðs1  s4 Þ

ð14Þ

where h4 is outlet enthalpy at the compressor and can be derived from isentropic efficiency. Entropy generation after the refrigerant performs isentropic expansion process (2–3) at expansion apparatus is expressed as follows: DSexp ¼ mr ðs3  s2 Þ

ð15Þ

For the temperature difference of heat exchange at the evaporator, entropy generation after the refrigerant performs isobaric expansion process (4–3) is expressed as DSeva ¼ mr ðs4  s3 Þ þ mw ðsevao  sevai Þ

ð16Þ

When the water flow through the evaporator, the change of entropy caused by the pressure drop is negligible, then the increase of the entropy is shown as follows: Z Z dQ CP w dT sevao  sevai ¼ ð17Þ ¼ ¼ CP w lnðTevao =Tevai Þ T T When the air flows through the fan coil, entropy generated from the chilled water and the air is shown as follows: DSFC ¼ 3ma2 CP a lnðTFCo =TFCi Þ þ mw CP w lnðTevai =Tevao Þ

ð18Þ

When the air flows through the condenser, and the refrigerant performs the isobaric condensing process (1–2), entropy generation is shown as follows: DScon ¼ ma1 CP a lnðTcono =Tconi Þ þ mr ðs2  s1 Þ

ð19Þ

The total exergy destruction of VAC yields as follows: DEx ¼ T0 ðDScom þ DScon þ DSexp þ DSeva þ DSFC Þ

ð20Þ

The objective function of total exergy destruction can be expressed as follows: min DEx ¼ T0 ð3maFC CP a lnðTFCo =TFCi Þ þ macon CP a lnðTcono =Tconi ÞÞ þ gm PI þ mr ðh4  h1 Þ

ð21Þ

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4. Thermoeconomic analysis of VAC system Thermoeconomic is a discipline that combines thermodynamic and economic analysis for the thermal system. In thermoeconomic optimization, the objective is either to minimize the unit product cost of the thermal system for a fixed output product or to maximize the product output amount for a fixed total cost of the system over its life cycle. The objective function consists of additive functions that evaluate energy source, equipment, and other associated costs in terms of money. A relationship between product cost and total cost of a thermal system can be written as follows [3]: X X X co Exo ¼ ci Exi þ Zn ð22Þ Ct ¼ o

i

n

where Ct is the life cycle cost, co is the unit product exergy cost, Exo is the annual exergy rate for output products, Exi is the annual exergy input from external sources, Zn is the annual cost of capital expenditure and other associated costs for any system (subscript n represents number of systems). In a VAC system, exergy input from outside the system is only electric energy which is completely used to do work, so unit cost of external exergy inputs equals to unit cost of electric energy, while the output products is only cooling capacity. In order to minimize the life cycle cost consisting of capital cost, maintenance cost and operating cost, annual exergy input from outsides is evaluated, because that it is very difficult to evaluate unit product exergy cost directly even though annual exergy rate is known. In the process of calculating input exergy, it is also difficult to calculate the input power of FCÕs fan, of condenserÕs fan and pump, which are important parts of input exergy. However, exergy input from outside the system can be obtained by means of Eq. (12), after exergy destruction of the system is calculated. Certainly, exergy output from the system can be calculated by means of cooling capacity and can be shown as Exo ¼ QFC ð1  T0 =TFCo Þ

ð23Þ

Generally speaking, for thermal systems with initial investment and operating cost over their lifetime, it is better to evaluate the life cycle cost of the system [3]. In engineering economics, the unit of time intervals for such purpose is usually taken as year. The capital recovery factor (CRF) is used to determine the equal amounts of n cash transactions for an investment and can be expressed as CRF ¼ A=P ¼ rð1 þ rÞn =½ð1 þ rÞn  1

ð24Þ

where A is called annuity, a series of equal amount cash transactions, P is the present value of the initial cost, r is the annual interest rate, and n is years of operation. Valero developed a correlation to evaluate the capital cost of the compressor [7], which is correlated with the mass flow rate of refrigerant, suction pressure, discharge pressure and the isentropic efficiency of compressor and is given as: pc ¼ c1 mr =ðc2  gsc ÞðP1 =P4 Þ lnðP1 =P4 Þ

ð25Þ

where c1 and c2 are constants determined from the market cost analysis. The isentropic efficiency of a scroll compressor [2] is fitted as follows:

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gsc ¼ 0:85  0:046667ðP1 =P4 Þ

479

ð26Þ

By combining Eqs. (21)–(26), the objective function of the life cycle cost of VAC over its life cycle is shown as min Ct ¼ ½c1 mr =ðc2  gsc ÞðP1 =P4 Þ lnðP1 =P4 Þ þ Ceva Aeva þ 3CFC AFC þ Ccon Acon þ Cadd ðCRFÞ þ Ch N fT0 ð3maFC CP a lnðTFCo =TFCi Þ þ macon CP a lnðTcono =Tconi ÞÞ þ gm PI þ mr  ðh4  h1 Þ þ ½QFC ð1  T0 =TFCo Þ g

ð27Þ

5. Constraints Although objective functions are obtained, their constrained conditions must be analysed in order to calculate the minimum of objective functions. Taking compressor as a control volume, and considering non-adiabatic loss and friction loss, the real input power of compressor is represented by PI ¼ mr ðh1  h04 Þ=gsc =gm

ð28Þ

where h04 is outlet enthalpy at the compressor performing the isentropic compression process. Assuming that the pressure loss of the refrigerant and air flowing through the condenser is negligible, the energy balance equation yields Qcon ¼ macon CP a ðTcono  Tconi Þ ¼ mr ðh1  h2 Þ

ð29Þ

Assuming that the pressure loss of the refrigerant and cooled water flowing through the evaporator is negligible, the energy balance equation is shown as Qeva ¼ mw CP w ðTevai  Tevao Þ ¼ mr ðh4  h3 Þ

ð30Þ

Total cooling capacity of VAC is constant, and cooling capacity of every fan coil is equivalent. On the assumption that the pressure loss of the air and cooled water flowing in the fan coil is negligible, then the energy balance equation is expressed by QFC ¼ 3maFC CP a ðTFCi  TFCo Þ ¼ mw CP w ðTevai  Tevao Þ

ð31Þ

In order to evaluate the surface area of heat exchanger, effectiveness of heat exchanger is firstly analysed and can be shown as follows e ¼ Qreal =Qmax

ð32Þ

where Qreal is the real heat capacity of the heat exchanger. Qmax is the maximum heat capacity of the heat exchanger, which is represented by Qmax ¼ Cmin ðThot  Tcold Þmax

ð33Þ

where Cmin is the smaller value of mCp in cold and hot fluids. ðThot  Tcold Þmax represents the potential maximum temperature difference of the inlet and the outlet of the heat-exchanger.

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When one of the cold and hot fluids changes its phase, the effectiveness of the heat-exchanger is expressed by e ¼ 1  expðNTUÞ

ð34Þ

When neither cold fluid nor hot fluid has phase change, the effectiveness of cross-flow heatexchanger can be shown as follows [8] " !( " # )# 0:78 0:22 C ðNTUÞ max C NTU max exp  1 ð35Þ e ¼ 1  exp Cmin Cmin where NTU represents the number of the heat transfer units, which is expressed by NTU ¼ UA=Cmin

ð36Þ

The refrigerant has phase change at the condenser, so combining Eqs. (29), (32)–(34) and (36) can be derived as follows: mr ðh1  h2 Þ ¼ ½1  expðUcon Acon =ðma1 Cpa ÞÞ macon Cpa ðT1  Tconi Þ

ð37Þ

The refrigerant also has phase change at the evaporator, so combining Eqs. (30), (32)–(34) and (36), we can obtain mr ðh4  h3 Þ ¼ ½1  expðUeva Aeva =ðmw Cpw ÞÞ mw Cpw ðTevai  T3 Þ

ð38Þ

On the assumption that the condensation of water vapor in the air flowing through the fan coil is negligible, combining Eqs. (31)–(33), (35) and (36), we have " !( " # )# 0:22 0:78 CmaxFC ðUFC AFC Þ CminFC ðUFC AFC Þ 1  exp exp  1 1:22 0:78 CminFC CmaxFC ðCminFC Þ ¼

QFC ðTFCi  Tevao Þ 3CminFC

ð39Þ

Cooling capacity of VAC system is kept constant, 30 kW, and its operation has to be limited to certain ranges of operating parameters. In the given condition, namely, indoor temperature at 22 C and outdoor temperature at 32 C, the operating ranges of the refrigerant and chilled water temperature are as follows: Considering outlet subcooling 5 C in the condenser and outdoor air temperature, condensing temperature is not lower than 37 C and higher than critical temperature 101 C. Considering indoor temperature, chilled water temperature is not higher than 22 C, of course, and cannot be lower than 0 C. Actually, according to chilled water temperature, evaporating temperature is determined and lower than 22 C.

6. Optimization procedure Based on the above thermodynamic property program and constraints, the thermodynamic and thermoeconomic optimization procedures are as follows:

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Step 1: To initialize the condensing temperature, the outlet air temperature to condenser, the outlet air temperature to FC, the inlet chilled water temperature to the evaporator, the inlet and outlet temperature difference to the evaporator, and evaporating temperature. Step 2: To claim the thermodynamic property program to evaluate condensing pressure, evaporating pressure, compression ratio, isentropic efficiency, discharge temperature for the compressor, enthalpy value (h1 , h2 , h3 , h4 ) and entropy value(s1 , s2 , s3 , s4 ) according to parameters derived from step 1, Eq. (26), outlet subcooling for the condenser and inlet superheated temperature for the compressor. Step 3: To evaluate the refrigerant mass rate, input power of the compressor and COP according to step 2 and cooling capacity. Step 4: To evaluate the air mass rate and heat transfer area of the condenser according to Eqs. (29) and (37). Step 5: To vary the outlet air temperature to condenser and repeat step 4. Step 6: To evaluate the water mass rate and heat transfer area of the evaporator according to Eqs. (30) and (38). Step 7: To evaluate the air mass rate according to Eq. (31) and heat transfer area of FC by means of iteration method according to Eq. (39). Step 9: To keep the inlet and outlet temperature difference constant, vary inlet chilled water temperature to the evaporator and repeat steps 6 and 7. Step 10: To keep inlet chilled water temperature constant, vary the inlet and outlet temperature difference to the evaporator and repeat steps 6 and 7. Step 11: To vary evaporating temperature and repeat steps 2–10. Step 12: To vary condensing temperature and repeat steps 2–10. Step 13: To calculate all possible exergy destruction and life cycle cost according to the above obtained results, Eqs. (21) and (27), and select minimum as thermodynamic and thermoeconomic optimization design respectively.

7. Results of optimization To carry out comparisons between thermodynamic and thermoeconomic optimization, the normal system is designed basing on the following design parameters: • Refrigeration system: condensing temperature ¼ 49.50 C; evaporating temperature ¼ 3.00 C; temperature of chilled water entering the evaporator ¼ 12.00 C; temperature of chilled water leaving the evaporator ¼ 7.00 C. • Outdoor conditions: dry-bulb temperature ¼ 32.00 C; wet-bulb temperature ¼ 24.00 C. • Indoor conditions: dry-bulb temperature ¼ 22.00 C; relative humidity ¼ 50.00%. Assuming the operating period is 15 years, with an annual interest rate of 10%, operating hours per year is 2500 h, and electricity price is 0.5 RMB Yuan/kW h, Table 2 shows thermodynamic optimization, thermoeconomic optimization, and standard design results. It can be seen that compression ratio reduction leads to remarkable increase of input power of the compressor and its

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Table 2 Results obtained for thermodynamic, thermoeconomic optimization and standard design Parameters

TDOD

TEOD

SDD

Condensing temp. (C) Evaporating temp. (C) Compression ratio Outlet air temp. to condenser (C) Inlet water temp. to evaporator (C) Outlet water temp. to evaporator (C) Outlet air temp. to FC (C) Area of condenser (m2 ) Area of evaporator (m2 ) Total area of FC (m2 ) Refrigerant mass rate (kg/s) Air mass rate in condenser (kg/s) Water mass rate in evaporator (kg/s) Air mass rate in FC (kg/s) Compressor power (kW) COP Operating cost of compressor (Y/yr) Life cycle cost (Y/yr) Exergy destruction (kJ/h)

42.00 11.02 2.50 35.0 15.00 13.00 14.00 42.29 21.63 186.81 0.19 12.25 2.38 1.24 6.66 4.50 8325.00 20586.85 20961.10

42.00 5.63 3.00 35.0 10.00 7.00 17.00 39.41 19.61 63.69 0.20 12.71 2.56 1.99 8.42 3.56 10525.00 18424.74 27781.44

49.50 3.00 4.00 36.0 12.00 7.00 16.00 29.94 5.84 76.19 0.22 10.36 1.43 1.66 12.44 2.41 15550.00 21844.57 38733.51



TDOD ¼ thermodynamic optimization design. TEOD ¼ thermoeconomic optimization design.  SDD ¼ standard design. 

operating cost which accounts for 4%, 57% and 71% of life cycle cost, respectively. Exergy destruction at thermodynamic optimization condition is 33% and 84% lower than that at other two conditions, respectively. So energy efficiency at thermodynamic optimization condition is the highest among three conditions. However, energy efficiency increase demands much larger heat exchange area than at other two conditions, in particular, area of FC 192% larger than that at thermoeconomic condition and 146% at standard design condition. So life cycle cost at thermoeconomic optimization condition is the lowest among the three conditions. Fig. 2 compares initial investment at thermodynamic, thermoeconomic optimization and standard design conditions. It can be seen that initial capital cost at thermoeconomic optimization and that at standard design conditions are almost equivalent. However, at thermodynamic optimization, remarkable increase of heat exchange area of FC results in initial investment increase of FC which is 193% larger than that at thermoeconomic optimization. It leads to the largest initial investment at thermodynamic optimization condition, which is 29% larger than at thermoeconomic optimization condition. Fig. 3 compares exergy destruction obtained at thermodynamic, thermoeconomic optimization and standard design conditions as operating hours vary. Exergy destruction obtained at thermodynamic optimization and standard design conditions is kept constant. However, exergy destruction at thermoeconomic optimization exists in three stages. Exergy destruction of a system is determined by itself. Thermoeconomic optimization results in variation of its configuration and operating state, so exergy destruction varies. It can be seen that exergy destruction at thermo-

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483

Fig. 2. Initial investment comparison at three conditions.

exergy destruction(kJ/hr)

40000 35000 30000 25000 20000 SDD TEOD TDOD

15000 10000 0

500 1000 1500 2000 2500 3000 3500 4000 operating hours(hr)

Fig. 3. Exergy destruction vs. operating hours per year.

economic optimization is gradually close to that at thermodynamic optimization as operating hours increase. It indicates that thermoeconomic optimization gradually come close to thermodynamic optimization as operating hours increase. Fig. 4 shows the trends of increase of life cycle cost with the change of operating hours per year. Life cycle cost at standard design condition is sensitive to operating hours. Different from other two conditions, operating cost increase that results from operating hours change cannot be offset by variation of configuration and operating state of the system. As operating hours increase, life cycle cost obtained at thermoeconomic optimization condition is always the lowest among three conditions, though that at thermodynamic optimization gradually approaches it. Fig. 5 shows the trends of increase of life cycle cost with interest rate increase. Life cycle cost at thermodynamic optimization is sensitive to interest rate. Because its configuration and operating state is constant, increase of life cycle cost caused by the interest rate increase cannot be offset. So life cycle cost gradually deviates from that at thermoeconomic optimization. As interest rate increases, the thermoeconomic optimization design is more favorable to decrease life cycle cost than other two designs.

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life cycle cost(RMB Yuan/yr)

28000

SDD TEOD

23000

TDOD

18000 13000 8000 0

500 1000 1500 2000 2500 3000 3500 4000 operating hours(hr)

Fig. 4. Life cycle cost vs. operating hours per year.

35000

life cycle cost(RMB Yuan/yr)

SDD TEOD

30000

TDOD 25000 20000 15000 10000 0

0.05

0.1 0.15

0.2 0.25 0.3

0.35 0.4

interest rate

Fig. 5. Life cycle cost vs. interest rate.

8. Conclusions New formulas are developed to investigate thermodynamic properties of HFC134a on a basis of previous work. A new concept is introduced that exergy input into the system is substituted for the sum of exergy destruction and exergy output from the system. Thermodynamic and thermoeconomic objective functions of VAC system are developed based on second law and thermoeconomic analysis of VAC system. Optimization results indicate that thermodynamic optimization contributes to energy contribution reduction, but it unnecessarily leads to decrease of life cycle cost; on the contrary, life cycle cost at thermoeconomic optimization is lower than that at thermodynamic optimization. Thermodynamic optimization leads to initial investment increase. Although initial investment contributes to energy efficiency increase and energyconservation, too high investment is undesirable for consumers. At the same time, initial investment reduction leads to energy efficiency reduction and operating cost increase. Thermoeconomic optimization design considering various factors is favorable. Operating hours per year and interest rate has different effects on two optimizations. As operating hours increase, life cycle

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cost at thermodynamic optimization is gradually close to that at thermoeconomic optimization. However, as interest rate increases, the former gradually deviates from the latter.

Acknowledgement The research work of this paper is financially supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, PR China.

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